Physical and numerical study of strain burst of mine pillars

Article history: Strain burst is a spontaneous dynamic failure of rock that can cause serious injury to the miners and dam-Received 11 September 2015 age to the underground excavations. To simulate the strain burst in the lab, a steel beam was designedReceived in revised form 21 November 2015 and connected to the compression loading machine. The beam acts as an energy absorber and is in directAccepted 29 December 2015 contact with the rock specimen which is under uniaxial compression loading. Upon failure of the speci-Available online 11 January 2016 men, the absorbed energy in the beam is transferred to the rock specimen to simulate the strain burst in underground pillars. Based on the physical tests, rock fragment velocities of more than 4 m/s were mea-Keywords: sured using a high speed camera. The interaction between the steel beam and the rock was modeledStrain burstKinetic energy using a hybrid discrete-finite element computer program. The effect of different parameters such as pil-Physical testing lar’s length and diameter, friction coefficient between pillar and roof, compressive strength of pillar, rockScaling post-peak behavior, roof stiffness, and pillar and roof rock densities on the intensity of the strain burstNumerical modeling were studied. The strain burst intensity was defined as the kinetic energy of the simulated rock.Rock burst Dimensional analysis was applied to find relationships between the dimensionless parameters in the numerical simulation. The proposed scaling model together with the numerical analysis appears to be able to show the significance of different parameters involved in the strain burst. In particular, it is shown that the pillar diameter and its uniaxial compressive strength have significant impacts on the induced kinetic energy during a strain burst. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction rock (rock burst); energy release rate plays a critical role in rock burst. Based on Cook’s studies, rock burst occurs when an excess Rock burst is the dynamic failure of rock that poses serious energy becomes available during the post peak deformation stagethreat to the underground activities. This is particularly the case of rock. One of the first attempts to model rock burst in a roomin deep underground mining in which high in situ stresses and and pillar mining system was proposed by Salamon [7] who usedbrittle rocks are involved. Ortlepp and Stacey [1] based on source the stiffness matrix (K) of the mining layout together with themechanisms, categorized the field rock bursts as: strain bursting, slope matrix (A) of the complete load convergence relations of pil-buckling, face crushing, virgin shear in rock mass and reactivated lars to predict the stability of the rock structure. He showed thatshear on existing faults or discontinuities. They described the the stable situation is achieved if the system matrix K + A is posi-strain burst that is involved with violent ejection of sharp rock tive definite. Petukhov and Linkov [8] considered the interactionfragments as the most common damage mechanism observed in between a linear elastic rock mass with a softening material andunderground excavations. During a rock burst, rock particles can used some energy equations to introduce a criterion for the stabil-be ejected with a velocity of 8–50 m/s [2] which can cause fatal ity of the system. Burgert and Lippmann [9] studied models ofinjuries and damages to the underground equipment. Stacey translatory rock bursting in an idealized coal seam. A model mate-et al. [3] reported that during a rock burst, the thickness of the rial and a model technique were suggested. They divided the coalejected rock can be in the order of 1 m and hence supports for ahead of tunnel face to three regions: (1) Passive elastic zone, (2)the rock must be capable of absorbing the rock kinetic energy. Rock active elastic zone and (3) active plastic zone. Their model was ableburst had been known in mining since the 18th century; however to explain some of the observations in the field. Zubelewicz andit remained essentially a subject of qualitative study [4]. Cook [5,6] Mroz [10] considered rock burst phenomenon as a dynamicdiscovered the fundamental requirement for violent fracture of instability problem. In their approach, a dynamic perturbation was superimposed into the static solution of the problem and then the possibility of kinetic energy growth of the system as an ⇑ Corresponding author. indication of rock burst was investigated. E-mail address: hamed@nmt.edu (A. Fakhimi).

Rock burst has been considered as a problem of surface instabil- approach was used to define some dimensionless parameters thatity by some researchers. Biot [11] performed the pioneering work play important roles in strain bursting of the rock.on surface instability of a half space. Vardoulakis [12] used thebifurcation theory to analyze the rock burst as a surface instability 2. Experimental studyphenomenon. Bardet [13] used a finite element formulation tostudy rock burst as a surface instability problem. The bifurcation A soft steel loading frame was designed and attached to the MTSof the solution was detected by evaluating the eigenvalues of the loading machine to absorb and store some strain energy that cantangential stiffness matrix. Whyatt and Loken [14] utilized the be released when the post-peak regime of the rock is approached.boundary element method to simulate sudden dislocation along The steel frame which is made of two W5 16 steel profiles witha fault plane. Their model was able to explain some of the odd the yield strength of about 345 MPa is shown in Fig. 1. The frame isdynamic phenomena that are observed during the rock bursts. to represent the roof structure in a room and pillar mining system. Some researchers have investigated the phenomenon of rock The top of the frame is bolted to the loading machine cross-headburst experimentally. A double rock sample model was studied and the rock specimen is accommodated between the platen con-both physically and numerically by Chen et al. [15]. The physical nected to the bottom of the frame structure and the machine actu-sample was made of granite and marble specimens of cylindrical ator. Experimental tests were conducted on the frame structure toshape and was tested in uniaxial compression. From the results obtain its stiffness. Fig. 2 shows the load–deflection curve for theof the tests, they concluded that it may be possible to predict the frame structure which suggests that the stiffness of the structureoccurrence of rock burst when a sudden decrease of micro- is about 14.1 kN/mm.seismic rate occurs in one zone while the micro-seismic rate The experimental tests were conducted on the Pennsylvaniacontinues to increase in an adjacent zone. A true triaxial rock test blue sandstone which has the following average mechanicalsystem was used by He et al. [16] to study the rock burst. The lime- properties: Elastic modulus = 26.3 GPa, Poisson’s ratio = 0.15,stone specimen, 15 6 3 cm in dimension, was loaded initially uniaxial compressive strength = 110.9 MPa, and Brazilian tensilein three mutually perpendicular directions and then abrupt strength = 9.9 MPa. Rock specimens 25 mm in diameter andunloading of the minimum principal stress in one loading face 68 mm in length were used for strain burst testing. The tests werewas performed, creating a stress state and boundary conditions conducted under stroke control. Each test took about 20–30 min toin the rock sample relatively similar to those that exist at a tunnel finish; the applied displacement rate was 0.0025 mm/s. The resultsface. The physical tests by these authors showed the ejection of of the uniaxial compressive tests using the frame structure arerock fragments from the unloaded surface of rock that was inter- reported in Table 1. All tests were finished by violent failure of rockpreted as rock burst. Kuch et al. [17] simulated coal mine bumps specimens. A high speed camera was used to record the burstingusing a model material. Their experimental investigation showed event (Fig. 3a). During the strain burst of the rock specimens, thethat the scatter in the critical rock stress, necessary for bump initi- velocities of some rock fragments flying in the camera plane wereation, is due to variations of the post-peak stiffness of the material. In this paper, strain burst in pillars was studied by using a softloading system. Strain burst is a type of rock burst that is associ- 120ated with gradual accumulation of strain in rock. Uniaxial com- Loading y = 14.08x R² = 0.9955pression tests were conducted on sandstone specimens using this 100 Unloadingloading system to allow for accumulation of the strain energy 80and sudden release of this energy when the rock approached to Load (kN)

its post-peak regime. A high speed camera was used to measure 60

the peak particle velocity. In addition, a numerical model wasutilized for simulation of the rock burst. The rock was represented 40by a bonded discrete element domain while the loading system 20was modeled as a linear elastic body. Different parameters thatare involved in the induced dynamic rock fracture and strain burst- 0ing such as the loading system stiffness, the rock strength, the 0 2 4 6 8pillar dimensions, and the rock-loading system interface friction Deformation (mm)coefficient were investigated in this study. Furthermore, a scaling Fig. 2. Load–deflection data for the frame structure.

Particle Velocity (m/s)

Fig. 4. Measured rock fragments velocities vs. their masses.

calculated with the use of Adobe Photoshop and MATLAB. An Exi-lim Casio camera capable of video recording at a rate of 1000frames per second was used in the recording and once the video 14.1 kN/mm, which is consistent with the stiffness of the physicalof the test was complete, each frame was extracted and individu- frame structure (Fig. 2).ally saved in a file. The time difference between two consecutive The bonded particle model for the rock was calibrated using theframes was 2.083 ms; the video was recorded at a rate of 480 technics introduced by Fakhimi in [18] and [19]. As a result, theframes per second to obtain a better resolution. The sandstone micromechanical parameters for the discrete system werefragments identified to be approximately within the camera plane obtained: normal spring contact stiffness (Kn) = 2.2 107 N/m,were singled out in the Adobe Photoshop by whiting out the pixel shear spring contact stiffness (Ks) = 8.0 106 N/m, normal bondarea of the fragment area and then the background was erased (nb) = 5.1 N, shear bond (sb) = 27.1 N, friction coefficient (l) = 0.5with a black eraser (Fig. 3b). This made it easier for the MATLAB and genesis pressure = 5.9 GPa. As explained in [19], the genesisprogram to find the area and the x–y location of the center of mass pressure is the initial isotropic stress applied to the surroundingof that particular fragment. Hence by knowing the x–y values of a walls of the specimen to induce small overlap of the particles infragment center on two different frames, and the elapsed time contact. As a consequence of this small overlap, a more realisticbetween the two, the fragment velocity was found. The mass of bonded particle model can be generated for rock. The sphericaleach particle was estimated assuming a spherical shape for the particles were assumed to have a radius within the range 0.4–particle and its known density. Fig. 4 shows the measured velocity 0.8 mm with the average radius Rave = 0.6 mm. Using theseof some rock fragments versus the mass of the particles. As Fig. 4 micromechanical parameters, a uniaxial compression test was con-indicates, high particles velocities of 0.5–4.3 m/s were measured ducted on a cylindrical specimen 25 mm in diameter and 68 mm inin our experiments which are typical particle velocities during an height. The simulated model resulted in the elastic and strengthactual field rock burst. parameters that are in good agreement with those for the sand- stone (Table 2).3. Numerical modeling of strain burst The calibrated bonded particle model for the sandstone which is 25 mm in diameter and 68 mm in height was loaded through the The computer program CA3 [18] which is a hybrid discrete- frame structure (Fig. 5a). 51,800 spherical particles were used infinite element code for 3D simulation of geo-materials was used the specimen. To expedite the computational process, the speci-for the numerical modeling of the rock burst. The sandstone was men was loaded initially by applying a uniform vertical tractionsimulated as a bonded particle system which is made of spherical to the lower loading platen. The applied forces versus the numer-particles that are glued at the contact points to withstand the ical cycles for specimens with and without end friction are shownapplied stresses. The loading frame was modeled as a linear elastic in Fig. 6. The intensity of the traction was such that upon equilib-material using finite elements. The discretized frame together with rium of the structure, the specimen was subjected to about 70% ofthe simulated rock specimen is shown in Fig. 5a. A numerical test its compressive strength (path AB in Fig. 6). Subsequently, a verti-conducted on the simulated beam confirmed that its stiffness is cal velocity of 0.03 m/s (with a time step of 4.2 108 s or

(a) (b) (c)

Simulated bonded particle specimen μ' = 0 μ' = 0.18

Fig. 5. (a) Finite element model of the frame structure together with the bonded particle rock specimen, and the damaged specimen after the strain burst assuming theinterfaces between loading platens and specimen ends to have a friction coefficient (l0 ) of (b) zero, (c) 0.18.

Table 2Comparison between the elastic and strength parameters of the sandstone and the simulated material.

Fig. 6. Axial force vs. numerical cycles for two specimens 25 68 mm2 in dimension with and without end friction. The friction coefficient is shown with l0 .

0.12 108 m/cycle) was applied to the bottom of loading platen be exactly within the plane of the camera. Nevertheless, the phys-(paths BC and BC0 ). During these two stages of loading, a quasi- ical and numerical particle velocities are within the range observedstatic solution was achieved by using a damping coefficient of in actual rock bursts.0.7. The damping force in CA3 program is obtained by multiplying The velocity of the platen of the steel beam which is in directthe unbalanced force for each finite element node or each discrete contact with the top of the specimen is shown in Fig. 7a. The veloc-particle by the damping coefficient [20]. When the applied stress ities for situations with and without specimen end friction arewas about 90% of the rock compressive strength, the damping coef- shown. Note that the specimen with end friction fails at an axialficient was reduced to 10% to allow a dynamic simulation of the compression of qu = 121 MPa compared to qu = 109 MPa when therock-loading frame structure at failure point of the specimen. end friction is zero. This increase in rock strength results in greaterFig. 5b and c shows two damaged specimens following the strain stored strain energy in the beam and greater beam velocity. As aburst. In Fig. 5b, no friction was assumed for the interface between consequence, the maximum kinetic energy of the rock burst isthe loading platens and the specimen ends. On the other hand, a expected to be greater in the beam with end friction (Fig. 7b). Thisfriction coefficient of 0.18 [21] was used in Fig. 5c. Note how the is not the case as the friction at the specimen ends absorbs part ofintroduced friction coefficient and the end frictional forces have the beam energy. Furthermore, the ends frictional forces whichprotected the specimen ends; only the middle part of the specimen support the specimen ends put restriction on the kinematics ofis subjected to the bursting. The maximum particle velocities the damaged specimen (Fig. 5). Consequently, the numerical modelreported by the CA3 program for Fig. 5b and c are 11.4 and suggests that the rock burst intensity is reduced if the friction coef-9.8 m/s, respectively. These maximum particle velocities are ficient between the specimen ends and the loading platens is notgreater than those reported in Fig. 4 based on the actual physical zero.measurement. This discrepancy between the numerically calcu-lated peak particle velocity and the physical values should be 4. Dimensional analysisexpected; the numerical model does not incorporates a rate depen-dent micro-mechanical model and in the physical measurement, The kinetic energy of a failing pillar (Q) due to strain burst canthe particle with greatest velocity is hard to find and it may not be considered as a function of the following parameters:40 A. Fakhimi et al. / Computers and Geotechnics 74 (2016) 36–44

In which a, b, h are the dimensions of the roof (Fig. 8) and Er is the

elastic modulus of the roof material. Therefore, the last term in Eq. (3) can be written as: D Tributary area of pillar qu D4 qu D4 h ¼ 4 ð5Þ Kr Vr Er h b Eqs. (4) and (5) indicate that the thickness of the roof has a great a impact on the roof stiffness and consequently the intensity of the rock burst. Note that the roof thickness in Fig. 8 is not necessarily L the whole thickness of the overburden material in a mine; a joint that separates the immediate roof from the overburden material Pillar can dictate and define the effective roof thickness in our analysis. Based on Eq. (3), parametric studies were conducted using the beam-specimen model shown in Fig. 5a and the results are dis- cussed in the next sections of the paper. Fig. 8. A pillar and its tributary roof volume. 5. Rock pillar brittlenessQ ¼ f 1 ðqp ; qr ; K r ; V r ; b; l0 ; L; D; qu Þ ð1Þ

In Eq. (1), qp, qr, Kr, Vr, b, l0 , L, D, qu are pillar density, roof density, The rock pillar brittleness (b) in Eq. (3) is defined in the dimen-roof stiffness, tributary roof volume (equal to abh in Fig. 8), pillar sionless form as the ratio of the Kp to Kr. The Kp parameter is thebrittleness, friction coefficient between pillar and roof or floor, pillar post-peak slope of the force–displacement curve of the pillar.length, pillar diameter, and uniaxial compressive strength of pillar, To vary the rock pillar brittleness, the micro-mechanical param-respectively. In Eq. (1), the elastic properties of the pillar are not eters (such as normal and shear bonds and genesis pressure) in theexplicitly considered. In particular, the explicit effect of pillar elastic bonded particle system were modified. However, for the simplemodulus was ignored assuming that this parameter is approxi- contact bond model used in this paper, it was realized that the onlymately proportional to the uniaxial compressive strength of the pil- parameter that has noticeable impact on the Kp value is the frictionlar; in general as the elastic modulus of rock is increased, its coefficient between the particles (l). The effect of l on the post-uniaxial compressive strength is increased as well. Considering peak behavior of the simulated rock specimen with D = 25 mmthe 3 independent dimensions of force, mass and length, and the and L = 68 mm is shown in Fig. 9. Notice that as expected by10 involved parameters, the following 6 dimensionless parameters increasing the internal friction coefficient, more ductile behaviorcontrol the dimensionless kinetic energy of the pillar upon bursting: is realized and more energy is needed for complete failure of the ! specimen. It is interesting to note that the aspect ratio (L/D) of Q L qp Dq D3 ¼ f2 ; ; b; l0 ; u ; ð2Þ the pillar has a negligible effect on the Kp value; Kp/Kr (forqu LD2 D qr Kr V r Kr = 14.08 kN/mm) varies from 117 to 135 when L/D changes from 0.5 to 8 for l = 0.5. This finding is consistent with the obser- In the next sections of the paper and in [22], it has been shown vations in the previous work [24,25].that for the situation considered in this paper in which the mass ofthe beam in Fig. 5a (or the mass of the roof) is much larger than themass of the specimen (or the mass of the pillar), the last two 6. Numerical tests resultsparameters in Eq. (2) can be combined such that: ! To verify the appropriateness of Eq. (3) in describing the Q L qp q D4 induced kinetic energy in the specimen due to the strain burst, sev- ¼ f2 ; ; b; l0 ; u ð3Þqu LD2 D qr Kr V r eral numerical tests were conducted. Fig. 10a shows the variation of dimensionless kinetic energy (the expression on the left side Note that based on the theory of linear elastic plates [23], the of Eq. (3)) vs. the L/D of the specimen. In these tests, only the spec-roof stiffness in Fig. 8 can be written as: imen length was modified and a friction coefficient of l0 = 0.18 was 3 used for the interface of the specimen ends and the loading pla- Er hKr ð4Þ tens. Note that the dimensionless kinetic energy remained almost ab unaffected by changes in the specimen length (within L/D = 1–8) A. Fakhimi et al. / Computers and Geotechnics 74 (2016) 36–44 41

and only when the specimen aspect ratio is less than 1, it showed in the relatively identical qu values for these specimens. This strat-some sensitivity to the L/D parameter. This should be expected as egy helped to single out the effect the Kp on the kinetic energy.for low L/D values, the uniaxial compressive strength of the speci- In Fig. 11b, the variation of the dimensionless kinetic energymen increases and that causes more energy to be stored and deliv- with the friction coefficient between the specimen ends and theered to the specimen at the time of strain burst. The important loading platens is shown. Note that the dimensionless kineticsuggestion by Fig. 10a is that the kinetic energy of the pillar is energy is not affected by the friction coefficient unless the frictionapproximately a linear function of the pillar length for the L/D val- coefficient is close to zero. The role of the specimen ends frictionues within the range of 1–8 studied in this paper; longer pillars are coefficient is to confine the specimen ends which results in greatersubjected to more violent strain bursting. Note that the increase in material confinement at its ends and less induced kinetic energy.the intensity of the strain burst due to increase in the specimen Fig. 12 shows how the dimensionless kinetic energy is affectedlength is due to the freedom of a longer section (far away from by the 5th dimensionless parameter in Eq. (3). Notice that differentthe loading platens) of the specimen to the lateral movement symbols have been used in the figure to indicate the variation inand that a longer pillar can absorb greater elastic energy before different parameters. From Fig. 12, it appears that a linear equationfailure. Nevertheless, for very large pillar lengths, the dimension- can approximately fit the data points.less energy is expected to approach zero as the supplied energyfrom the roof is a finite value. 7. A simplified analytical model and discussion of the results Fig. 10b shows the variation of dimensionless kinetic energywith the ratio of pillar density to roof density. Note that irrespec- Consider the frame structure in Fig. 5a which is under the load Ptive of the change in the pillar or roof density, the data points fol- applied at its mid span through the rock specimen. Suddenlow a relatively linear trend. From this figure, it is concluded that removal of the applied load due to spontaneous failure of the rockreduction in the roof mass, causes a more violent bursting of the causes the strain energy in the linear elastic beam to transformpillar as the stored energy in the roof or beam can result in greater into kinetic energy, i.e.initial velocity when a lighter material is involved; this observation 1 1 P2supports the simplified energy approach in predicting the kinetic mr v 2r ¼ ð6Þenergy of the pillar burst as discussed in the next section. 2 2 Kr In Fig. 11a, the effect of the variation of Kp/Kr (for a fixed In Eq. (6), Kr is the beam (or roof) stiffness, vr is the beam velocity atKr = 14.08 kN/mm) on the dimensionless kinetic energy is shown. its mid span, and mr is part of the beam mass that can be consideredIt appears that there is a linear relationship between the dimen- as a lumped mass in Eq. (6) which is about one half of the wholesionless kinetic energy and Kp/Kr parameter. Note that as discussed beam mass. By substitution for P with respect to the uniaxial com-in the Section 5, in playing with the Kp parameter, the microme- pressive strength of rock (qu), we havechanical parameter l was varied which resulted in small changesin the uniaxial compressive strength of the specimens. The normal p2 q2u D4 v 2r ¼ ð7Þand shear bond between particles were slightly adjusted to result 16K r mr42 A. Fakhimi et al. / Computers and Geotechnics 74 (2016) 36–44

If the mass of the specimen (or pillar) is assumed to be small underground activities that are prone to the strain bursting, largecompared to the mass of the frame structure (mass of the tributary diameter pillars should be avoided. Numerical results in Fig. 13 con-volume of the roof), the specimen shows negligible resistance in the firm the linear relationship between the kinetic energy of the pillarimpact of the beam to the specimen top and hence the velocity vr is with the qu2 and D6.approximately equal to the velocity of the top of the specimen To reduce the possibility of rock burst in the mining engineer-(pillar). Therefore, an estimate for the kinetic energy (Q) of the ing, a technics called de-stressing is used. De-stressing is to movedamaged specimen or pillar is as follows: highly stressed zones some distance from the mining activities. The idea of de-stressing is not new, and this technique has been mp q2u 4 reported in the 1950s [26,27]. In general, three de-stressing tech-Q D ð8Þ mr K r niques are available: blasting, drilling, and water infusion/hydrau- lic fracturing. Blast de-stressing or preconditioning has beenIn Eq. (8), mp is the mass (or part of the mass involved in the burst) successfully used in the South African gold mines. Grodner [28]of the specimen (or pillar) and is to show that Q is proportional to reports that rock preconditioning by detonating explosives in thethe right hand side expression. For a pillar and the attached roof in confined rock mass ahead of the mining face transfers the stressesFig. 8, the kinetic energy becomes: further away and effectively unloads the immediate face area. Lqp q2u D6 To study the effect of preconditioning on the induced kineticQ ð9Þ energy in the numerical simulation, drilling approach was utilized; abhqr K r in the circumferential area of the bonded particle specimen 2.5 (di-Based on Eq. (9), it is easy to see that the dimensionless kinetic ameter) 6.5 (height) cm2 in size, circular holes within the rangeenergy has a linear relationship with the second and fifth parame- of 0–0.3 cm in diameter and 0.5 cm in depth in a square patternters in Eq. (3), which is consistent with the numerical results shown of 1.57 1.57 cm2 were generated (Fig. 14). Two sets of numericalin Fig. 10b and 12. The shortcoming of Eq. (9) is that it does not tests were conducted. In the first set, the uniaxial compressiveinclude the other involved parameters which were identified strength of the simulated specimen was allowed to reduce due tothrough dimensional analysis and are reported in Eq. (3). Notice the presence of the holes. As Fig. 15a shows, in this case, thethat in Eqs. (3) and (9), the two parameters that have the greatest induced kinetic energy reduced linearly as the diameter of theimpact on the rock burst energy are the specimen diameter and holes is increased. In the second set of the numerical tests, thethe uniaxial compressive strength of rock (pillar). In particular, dou- normal bond and shear bond at the contact points of the particlesbling the specimen or pillar diameter can increase the rock burst were increased proportionally such that the uniaxial compressiveenergy by about two orders of magnitude. This suggests that in strength was not affected by the presence of the holes. The A. Fakhimi et al. / Computers and Geotechnics 74 (2016) 36–44 43

due to the reduction in uniaxial strength of the specimen; field pre-

conditioning mostly targets the rock strength in the strain burst region through which the potential for sever rock bursts is diminished.

1.57 cm 8. Conclusion

A steel frame structure was designed to act as a soft loading sys-

tem in uniaxial compression testing of sandstone specimens. The physical uniaxial tests showed that violent failure can be captured by using this testing configuration. High speed camera photogra- phy showed particle velocities of the failed specimen in the order of 4–5 m/s which should be expected in an actual field rock burst. The physical tests were mimicked by using a linear elastic finite element model for the frame structure while the rock was simu- 1.57 cm lated by a bonded particle discrete element system. Dimensional analysis was implemented to predict the relationship between the induced kinetic energy and the involved parameters. It was shown that the pillar (specimen) diameter, pillar length, roof stiff- 1.04 cm ness, post-peak pillar behavior, roof-pillar interface friction coeffi- cient, pillar and roof rock densities, tributary volume of the roof, and uniaxial compressive strength of pillar are contributing factorsFig. 14. The hole (3.0 mm diameter) pattern in the simulated rock specimen to into the induced kinetic energy of the bursting pillar. In particular,reduce the induced kinetic energy of strain burst. the pillar diameter and its uniaxial compressive strength have greatest impact on the severity of the strain burst. The numericalvariation of the kinetic energy with the hole diameter is shown in model confirmed that preconditioning of the pillar by drilling canFig. 15b. Note that in this latter case, even though the data points be used as a tool to diminish the intensity of the strain burstingshow some small scatter, the change in kinetic energy with the in a pillar and that the reduction in the kinetic energy of the rockhole diameter seems to be negligible. This observation suggests burst in this situation is mostly due to the reduction of uniaxialthat the reduction in the kinetic energy in the first case is mostly compressive strength of pillar through the generated holes.